On the Necessity of Multi-Domain Explanation: An Uncertainty Principle Approach for Deep Time Series Models

TL;DR

This paper argues for the importance of multi-domain explanations in deep time series models, using an uncertainty principle from signal processing to identify when time and frequency domain attributions differ significantly, thus requiring both for comprehensive interpretation.

Contribution

It introduces the application of the uncertainty principle to XAI, providing a criterion to determine when time and frequency domain explanations should both be presented for better understanding.

Findings

Frequent violations of the uncertainty principle across datasets and models.

Existing explanations often focus solely on the time domain, missing important features.

Multi-domain explanations are necessary for comprehensive interpretation.

Abstract

A prevailing approach to explain time series models is to generate attribution in time domain. A recent development in time series XAI is the concept of explanation spaces, where any model trained in the time domain can be interpreted with any existing XAI method in alternative domains, such as frequency. The prevailing approach is to present XAI attributions either in the time domain or in the domain where the attribution is most sparse. In this paper, we demonstrate that in certain cases, XAI methods can generate attributions that highlight fundamentally different features in the time and frequency domains that are not direct counterparts of one another. This suggests that both domains' attributions should be presented to achieve a more comprehensive interpretation. Thus it shows the necessity of multi-domain explanation. To quantify when such cases arise, we introduce the uncertainty principle (UP), originally developed in quantum mechanics and later studied in harmonic analysis and signal processing, to the XAI literature. This principle establishes a lower bound on how much a signal can be simultaneously localized in both the time and frequency domains. By leveraging this concept, we assess whether attributions in the time and frequency domains violate this bound, indicating that they emphasize distinct features. In other words, UP provides a sufficient condition that the time and frequency domain explanations do not match and, hence, should be both presented to the end user. We validate the effectiveness of this approach across various deep learning models, XAI methods, and a wide range of classification and forecasting datasets. The frequent occurrence of UP violations across various datasets and XAI methods highlights the limitations of existing approaches that focus solely on time-domain explanations. This underscores the need for multi-domain explanations as a new paradigm.